Building the Language of Mathematics for Students Mathematically proficient students communicate precisely by engaging in discussions about their reasoning using appropriate mathematical language. The terms students should learn to use at each grade level with increasing precision are included in this document. Mathematics can be thought of as a language that must be meaningful if students are to communicate mathematically and apply mathematic productively. Communication plays an important role in helping children construct links between their formal, intuitive notions and the abstract language and symbolism of mathematics; it also plays a key role in helping children make important connections among physical, pictorial, graphic, symbolic, verbal, and mental representations of mathematical ideas. Curriculum and Evaluation Standards for School Mathematics, the National Council of Teachers of Mathematics (p. 26)

Mathematical vocabulary however should not be taught in isolation where it is meaningless and just becomes memorization. We know from research that meaningless memorization is not retained nor will it help build the deep understanding of the mathematical content. The students must be provided adequate opportunities to develop vocabulary in meaningful ways such as mathematical explorations and experiences. Students should be immersed into the mathematical language as they experience rich high-level tasks. As student communicate their thoughts, ideas, and justify the reasonableness of their solutions the mathematical language will begin to evolve. Student will then build the depth of understanding needed with mathematical vocabulary and content to empower them to be successful in mathematics. Questions or feedback please contact: [email protected] or [email protected]

Second Grade Operations and Number and Measurement Geometry Algebraic Thinking Operations in Base Ten and Data Represent and solve problems Understand place value. Measure and estimate Reason with shapes and involving addition and hundreds, tens, ones, skip count, base-ten, lengths in standard their attributes. subtraction. number names to 1,000 (e.g., one, two, units. attribute, feature, angle, side, add, subtract, more, less, equal, thirty, etc.), expanded form, greater than about, a little less than, a triangle, quadrilateral, square, equation, putting together, (>), less than (<), equal to (=), digit, little more than, longer, rectangle, trapezoid, pentagon, compare hexagon, cube, face, edge, North Carolina Department of Public Instruction (DRAFT) July 2013 taking from, taking apart, Use place value understanding and shorter, measure, standards vertex, surface, figure, shape, addend, comparing, unknown properties of operations to add and units, units, customary, closed, open, partition, equal Add and subtract within 20. subtract. metric, inch, foot, size, equal shares, half, halves, add, subtract, sum, more, less, fluent, compose, decompose, place value, centimeter, tools, ruler, thirds, half of, a third of, whole, equal, equation, putting digit, ten more, ten less, one hundred more, meter, centimeter, ruler, two halves, three thirds, four yardstick, meter stick, fourths, rows, columns together, taking from, taking one hundred less, add, subtract, sum, equal, measuring tape, estimate, From previous grades: circle, apart, addend addition, subtraction sums, differences square, sphere, half-circle, Work with equal groups of Relate addition and quarter-circle, cone, prism, objects to gain foundations subtraction to length. cylinder, trapezoid for multiplication. inch, foot, yard, odd, even, row, column, centimeter, meter, ruler, rectangular array, equal, yardstick, meter stick, addend, equation, sum measuring tape, estimate, length, equation, number line, equally spaced, point, addition, subtraction, unknown, sums, differences, measure, standard units, customary, metric, units, sums, differences Work with time and money. time, hour hand, minute hand, hour, minute, a.m., p.m., o’clock, multiples of 5 (e.g., five, ten, fifteen, etc.), analog clock, digital clock, quarter ‘til, quarter after, half past, quarter hour, half hour, thirty minutes before, 30 minutes after, 30 minutes until, 30 minutes past, quarter, dime,

North Carolina Department of Public Instruction (DRAFT) July 2013 nickel, dollar, cent(s), $, ¢, heads, tails Represent and interpret data. collect, organize, display, show, data, attribute, sort, line plot, picture graph, bar graph, question, category, chart, table, most, least, more than, less than, about, same, different, measure, inch, foot, yard, centimeter, meter, length

North Carolina Department of Public Instruction (DRAFT) July 2013